How to: DIY disposable cloth napkins

Have to share this idea.

The other day I went to my happy place, Anthropologie, and in the sale section they had a sort of cloth napkin that was disposable and that you could tear off a roll. Not with snaps or anything, just a roll of cheap cotton fabric in cute gingham prints that you could tear. Kind of like an upscale picnic item. I was intrigued but I didn't bite. But at home, I did have, waiting for me to do something with them, two worn out pillow cases.

You know when sheets or pillow cases get so thin there is no point in mending them? A sheet might become a tarp for spray painting or a pillow case might become rags for cleaning. Once I made waxing strips out of an old sheet and and old pillow case. But we currently have enough rags and tarps and waxing strips so these pillow cases were just waiting. I couldn't throw them away, but I didn't have much time to deal with them either.

Soooo...idea! I quickly tore each pillow case

Genius

Kadin was working on a math problem for his homework and asked for my help. He actually didn't bring the problem home but said he remembered it. He tried to explain it to me and it was something like this:
A jail has 100 cells. The guard comes in the first day and unlocks all the cells. On the second day he locks all the cells that are multiples of two. On the third day he unlocks all the cells that are multiples of 3 (or something like that, Kadin wasn't exactly sure) and so on. The question was, on the 100th day, which cells would be unlocked?

So we agreed there must be a pattern. Kadin had gone through and figured out